He would initiate a verbal confrontation with Andrew and say things like, You are not my son. Later, he'd clarify that he meant Andrew doesn't act like his older brother does. Another example: You didn't call me last week, so I'm not going to help you out today. The one blessing is that both boys love each other. I believe children should know they are loved by their parents. They should not have to continually prove they are worthy of their parent's love.
I think the first thing you both need to do, though, is to adjust your attitudes in the situation. I know this sounds a bit accusatory, but hear me out. You describe Emma, who is a child, as a "spoiled brat." You don't just see her behavior as bratty, but her personality as bratty and somewhat irredeemable. Children can pick up on when they aren't liked, and-like it or not-when you married Diana, you also made a commitment to Emma that includes being there.